Problem: If $x \oplus y = x+7y$ and $x \barwedge y = xy+3x-y$, find $3 \oplus (1 \barwedge -6)$.
Explanation: First, find $1 \barwedge -6$ $ 1 \barwedge -6 = -6+(3)(1)-(-6)$ $ \hphantom{1 \barwedge -6} = 3$ Now, find $3 \oplus 3$ $ 3 \oplus 3 = 3+(7)(3)$ $ \hphantom{3 \oplus 3} = 24$.